Mayor Vincent C. Gray is expected to begin filling those vacancies Friday, a move that could redirect the spotlight off university system president Allen Sessoms, who is under fire for questionable travel expenses.

Mr. Sessoms continues to defend himself by saying that he travels for the same reasons other university presidents travel — because of partnerships, symposiums and conferences, and to win friends and raise the university’s image.

The mayor has said that even under the cloud of Mr. Sessoms’ travel expenditures, he doesn’t want to insert himself into the day-to-day operations at UDC.

“My preference is to let the trustees govern,” he has said.

Several council members who grilled Mr. Sessoms and Mr. Askew at Tuesday’s oversight hearing on UDC made similar remarks.

“I want to examine the totality of the university’s operations,” said Yvette Alexander of Ward 7. At-large member Sekou Biddle said he was in search of the “best way forward.”

Former mayor Marion Barry of Ward 8 said his colleagues shouldn’t get “distracted,” adding that “we wrestled with Mayor [Adrian M.] Fenty about the board [vacancies.] Let’s look at the whole picture.”

And Mr. Brown, an at-large council member, said the mayor’s forthcoming nominations would help steer the board toward important matters, including the restructuring plan already under way and fundraising for an institution whose students are heavily subsidized.

“Fundraising has to be the No. 1 priority, as it is with other institutions of higher learning,” he said.

Mr. Askew agreed, saying the board needs members who have “certain areas of expertise and resources to raise money.”

Mr. Brown said names with fundraising and expertise gravitas also include Mr. Leonsis, who owns both the Washington Wizards and the Washington Capitals, and Mr. Johnson, who owns the Charlotte Bobcats, founded BET and now heads his own film production and real estate development firm.

Mr. Gray’s picks likely will not face the same finger-wagging as those of Mr. Fenty, whose UDC nominees were summarily rejected by the council when Mr. Gray was its chairman.

“I have reached out to the mayor and he will be sending names to the council soon,” Council Chairman Kwame Brown said Tuesday. “He understands the importance of moving quickly on this matter, I will move the nominees quickly for hearing[s] once they are received.”